# Interpreting a R^2 in light of a regression coefficient

• Feb 25th 2013, 10:01 AM
kingsolomonsgrave
Interpreting a R^2 in light of a regression coefficient
Interpreting a R^2 in light of a regression coefficient

If I have a regression coefficient of say 0.5 and a R^2 of 0.01 how do I interpret this?

The dependent variable increases by 0.5 for a one unit increase in the independent variable and at the same time the relationship explains only one percent of the overal variance of the dependent variable.

Is that correct?

Also, if we want to decide if an the independent variable is a major cause in variation of the dependent variable then having a low R^2 should indicate that the independent variable is NOT a major cause?

What if the R^2 score is relatively low (like 0.01) but the coefficient of the regression is relatively high ( like 3.9) ? How would you interpret that?

thanks!
• Feb 25th 2013, 06:37 PM
chiro
Re: Interpreting a R^2 in light of a regression coefficient
Hey kingsolomonsgrave.

The R^2 gives an indication of the fit of the model in terms of a linear fit.

You need to put the data into context to see if the data have a non-linear relationship. If they do, then it would be appropriate to find a good regression model or to transform the data so that it looked linear.

If however the data seem to be un-correlated (no matter how you look at it), then it means that you will probably conclude that there is no strong relationship between the variables and that a model can't be adequately fit.

Its always important that the R^2 value is really only useful for interpreting a linear correlation and not a general one.